|100 metres (328 feet) is the max length for Cat5 but I highly recommend you not exceed 90 metres as attenuation can begin over that distance and degrade the signal.|
Depth doesn't matter. Bury it 100 feet down if you want....but don't forget when you're computing total length of your cable that if you go down, you also have to come back up and both of those changes are added into the total length of the line.
ie: if you're covering 288 feet and you go down 6'....add 12' to total length of cable so you have a total of 300'....plus, add 2 or 3 feet to each end so you have some slack to play with.
I would highly recommend you use PVC pipe or something like it if possible for a couple of reasons. One, protection from the elements as someone else mentioned above (ie: water on a cracked casing is not good). Two, if you need to pull another cable in the future, having ready conduit simplifies doing so. NOTE: wizards advice was good, pull one or two extras in case of future need.
You'll need a long enough fish tape to make the pull. I also highly recommend you pull a piece of twine along with the wires and tie it at both ends in case you need to pull more cable in the future......with the twine in place, no fish tape is needed.
You're way south of me down there in Minnesota....I live in northern Alberta. Frost goes down about 6' come winter, you would probably want to put your cable below that depth, in fact, I recommend it. Frost could break the PVC and possibly wreck the casing on the cable.
Last but not least...If possible, you might want to go with a fibre optic cable between buildings as you can have much longer distance between points. From the sounds of it, you're already pushing the limits of Cat5 even taking the shortest route.